Today I had a continuation of a call with tech support.  The guy on the phone seems decent, so I ask, “based on what you see, what’s the best way to fix this problem?”

“Manually migrate all the data out of the system, then manually migrate it back into a new one, finally reconnect all the users to the new system.  It should only take a week.”

Sadly he’s right.  I’m still going to go one more shot at the “fix the corruption during an outage window” option first, since we’re moving OFF of this system by the end of the summer.